Dunno that auto vs. manual has anything to do with it, except that Ford does use different mufflers for auto vs. manual GTs, at least on S197s.
I can tell you that I decided about five minutes after buying my '08 automatic that, in my view, there are way too many wrong-wheel-drive, four cylinder econoboxes running around with duals (well, splitters really) for any Mustang to have a single, rusty tailpipe poking out on one side.
I went with a set of manual GT takeoffs myself. I think it improved both the looks and the sound substantially. As far as performance, eh, who knows? Maybe a minor improvement, along with slightly better gas mileage.
The downsides for me were; high cost (crazy expensive hangers), drone and buzzing inside (fairly well controlled with insulation under the rear seat and trunk mat), and annoyed neighbors.
Apparently quite a few folks have gone with single GT takeoffs. Very quick, easy, and usually dirt cheap swap for better sound and a nice polished exhaust tip.